Empirical L2L2-distance lack-of-fit tests for Tobit regression models

Standard Tobit regression models assume a linear relationship between the partially observed response variable and the predictors, while applications often see some nonlinear connections. This paper proposes an empirical L2L2-distance lack-of-fit test to check the adequacy of the presumed parametric form for the regression function in Tobit regression models. The proposed test statistic is shown to be asymptotically normal, consistent against some fixed alternatives, and has nontrivial power for some local nonparametric alternatives. Simulation studies are conducted to assess the finite sample performance of the proposed test.